Then he makes the rather obvious mistaken assumption that Lokir was going to be returned to Rorikstead, and preferred death. He ran away because he didn't want to be executed, not because he feared going back.

What is interesting about Lokir is that if he was fleeing to Hammerfell, he was going entirely the wrong way if he were captured with the Dragonborn and the Stormcloaks near the Darkwater. The quickest way to Hammerfell from Rorikstead is south through Falkreath hold, not east across Whiterun and into the Rift.

One of my questions is where is there any evidence Lokir lived in Rorikstead? No family, no house.

My poorly researched theory is Lokir lived most of his childhood Rorikstead but his parents died and he was sent to Honorhall Orphanage in Riften for some time. Never being adopted, he was kicked out at adulthood and spent some time living in the Ratways among the thieves and homeless of Riften until he tried to leave during the civil war. His plan, to steal a horse and travel to Hammerfell instead of a family-less Rorikstead, was busted and he was sent with the passing through execution line to Helgen.

He also says that Rorikstead must be old because "Ragnar the Red" is a very old song... While that certainly may be true, the best evidence we have for Rorikstead being REALLY old is it's listing in Holdings of Jarl Gjalund, which Farengar desribes as having "terminology of the First Era" or something like that.

Edit: However, as ESO doesn't have it on the map nor makes no mention of it (I don't play it, so someone can debunk me) and that took place 2E 582 and may or may not be canon... well... I guess there's that to take in consideration.